
where \(F(x)\)  and \(G(x)\)  are arbitrary functions of \(x\)  and are called the super-rotations and the super-translations respectively. The generators \(\mathcal {L}_n\)  and \(\mathcal {M}_n\)  (with \(n\in \mathbb {Z}\) ) of these transformations in the space of ordinary scalar-valued functions give rise to the following infinite-dimensional algebra known as the \(1+1\) D Carrollian/Galilean [1]} conformal algebra:
\(\left[\mathcal {L}_n\hspace{2.84526pt},\hspace{2.84526pt}\mathcal {L}_m\right]=i(n-m)\mathcal {L}_{n+m}\hspace{7.11317pt};\hspace{7.11317pt}\left[\mathcal {L}_n\hspace{2.84526pt},\hspace{2.84526pt}\mathcal {M}_m\right]=i(n-m)\mathcal {M}_{n+m}\hspace{7.11317pt};\hspace{7.11317pt}\left[\mathcal {M}_n\hspace{2.84526pt},\hspace{2.84526pt}\mathcal {M}_m\right]=0\) 
